SIgned MOdels for Network Analysis

The software package `SIMONA' is designed to solve maximum-entropy models for signed graphs and generate the related ensembles.

The software package `SIMONA' (SIgned MOdels for Network Analysis) is designed to solve maximum-entropy models for signed networks and generate the related ensembles.

Sampling random graphs with given properties is crucial for network analysis, as they represent benchmarks against which empirical observations must be compared for detecting the fundamental patterns shaping real-world networks. Microcanonical implementations of signed null models, which generate graphs that strictly adhere to the specified constraints, are prone to biases and inefficiencies. To avoid these limitations, here we consider the exact canonical framework induced by Shannon entropy maximization, ensuring that the enforced constraints are realized on average. More specifically, we consider graphs whose edges are associated with a +1, a -1 or a 0 and propose an iterative method to correctly sample a set of four ensembles of signed networks, i.e. those associated with both the free-topology and the fixed-topology versions of the Random Graph Model and the Configuration Model: in the former case, signs are shuffled along with the edges while, in the latter, signs are permuted on a set of connections that, instead, are kept fixed. In words, the benchmarks belonging to the first basket are designed to model situations where agents can choose both with whom and how to interact while the benchmarks belonging to the second basket are designed to model situations where agents can solely choose how to interact. Since our approach relies upon exact maximum-entropy distributions, it is inherently unbiased, even for highly heterogeneous networks.

For what concerns the theoretical methodology lying at the basis of the entropy-based canonical models, see:

[1] Park, J. & Newman, M. E. J. Statistical mechanics of networks. Phys. Rev. E 70, 66117 (2004).

[2] Squartini, T. and Garlaschelli, D. (2011). Analytical maximum-likelihood method to detect patterns in real networks. New Journal of Physics, 13:083001.

The software package `SIMONA' implement both binary, undirected and binary, directed, signed models.

The binary, undirected, signed models are introduced and solved in the paper Testing structural balance theories in heterogeneous signed networks, co-authored by Gallo, Garlaschelli, Lambiotte, Saracco, Squartini and published on Communications Physics 7, 154 (2024).

The binary, directed, signed models are introduced and solved in the paper Patterns of link reciprocity in directed, signed networks, co-authored by Gallo, Saracco, Lambiotte, Garlaschelli, Squartini, arXiv:2407.08697 (2024).

The binary, undirected, bipartite, signed models are introduced and solved in the paper Statistically validated projection of bipartite signed networks, co-authored by Gallo, Saracco, Squartini, in preparation (2025).

Please cite the paper(s) above every time you show results obtained by employing this routine.